I don't think off-duty cops should have anymore right to carry some place more than a permit holder.

Here in MI we've had it set up so CPL carriers can go into an establishment that serves alcohol but only if the majority of the establishment's income comes from other than alcohol. We've had our shall-issue law for probably more than a decade now, and no bar has ever been turned into a shooting gallery.....well at least not by a lawful gun owner.